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Re: long time no see

I must say that I am unfamiliar with this way of speaking the language.
I've tried to explain the way to myself but I couldn't.

I'd say

It's been a long time since I saw you. (Both of them know when they last met)

"It's been a long time since" could be the definite adverb of time for the simple past "saw" in the latter part.
On the other hand "I've seen you" in the latter part can not be used with the definite adverb of time.